Title: Product mixing in groups 


Abstract:
Let A, B, C be subsets of the special unitary group SU(n) of Haar measure
≥ e^{−n^1/3}. Then ABC = SU(n). In fact, the product abc of random elements
a ~ A, b ~ B, c ~ C is equidistributed in SU(n).
This makes progress on a question that was posed independently by Gowers
studying nonabelian variants of questions from additive combinatorics and settles
a conjecture of physicists studying quantum communication complexity.
To prove our results we introduce a tool known as ‘hypercontractivity’ to the
study of high rank compact Lie groups. We then show that it synergies with their
representation theory to obtain our result.


Recording Link: https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e15aab68-0f6d-45e1-9fdf-b31300cf245b